Soak the tapioca pearls in 2 cups of room temperature water for at least 30 minutes, or overnight.
Drain the soaked tapioca and set aside.
In a medium saucepan, bring the milk and salt to a simmer over medium heat, stirring occasionally.
Add the drained tapioca pearls to the milk and reduce the heat to low. Cook, stirring frequently, for about 45 minutes, until the tapioca pearls become translucent.
In a small bowl, whisk together the sugar and eggs.
Temper the egg mixture by slowly adding a bit of the hot tapioca into the eggs while whisking constantly.
Return the tempered egg mixture to the saucepan and continue to cook for an additional 10 minutes or until the pudding thickens, stirring often.
Remove from heat and stir in the vanilla extract.
Transfer the pudding to a serving bowl or individual cups and let cool. Serve warm or chilled.